Displacement Amplification Factor Research Articles

Estimation of effective damping ratio for cast-in-place tunnel-form system and evaluation of its role in performance point prediction

The extensive time and computational effort are primary challenges in nonlinear dynamic analysis of tunnel-form concrete systems. These challenges lead engineers to resort to simpler, pushover-based analyses, inherently based on estimating the seismic performance point of the system. Technical literature review indicates that no study has yet rigorously evaluated the accuracy of existing methods for estimating the performance point of tunnel-form systems. To eliminate potential ambiguities, in this study, the seismic performance point of the system under design basis earthquake (with a 475-year return period) has been calculated using three different methods (i.e., displacement coefficient, capacity spectrum, and displacement amplification factor), and compared with the results of accurate nonlinear time-history analysis. In the range of 5-, 7-, and 10-story models studied, the results indicate the inefficiency and insufficiency of the mentioned methods. Investigations reveal that while the capacity spectrum method provides better results, but its process is lengthy, and the displacement coefficient method significantly overestimates the performance point (with more than 80 % error). It was also evident that the displacement amplification factor underestimates the performance point and contradicts the direction of confidence. Based on observations, the use of all three methods for the tunnel-form system requires modifications. The calculated values of effective damping ratio for the tunnel-form system explicitly indicate type A behavior according to the ATC-40 classification. By presenting this parameter in a multi-level format, the shortcomings of both capacity spectrum and displacement coefficient methods are easily addressed. Referring to the results, the calculated value of the displacement amplification factor in the system exceeds the recommended value by the seismic design code, and by adjusting it, satisfactory responses can be obtained in the method based on the displacement amplification factor. Finally, introducing the “probable performance interval” parameter, recommending its use instead of the “performance point” parameter in assessments by pushover analysis is suggested. This parameter is applicable with all three mentioned methods and has been introduced in this study as a desirable factor in compensating for inherent uncertainties related to future earthquakes.

Seismic design parameters of double-layer diamatic domes

The effect of past earthquakes (e.g., the 1995 Kobe and 2016 Kumamoto earthquakes) on the space structures revealed the fact that the assumption of the invulnerability of these structures is incorrect despite their light self-weight and high degree of redundancy, and space structures may suffer severe damage during strong ground motions. Therefore, special attention should be paid to the design of this type of structure in high seismic-risk regions. Nevertheless, the existing seismic design codes have not provided the seismic design parameters (i.e., the seismic response modification factors), including the behavior factor, R, and the displacement amplification factor, Cd for space structures. This research aims to extract the seismic design parameters of double-layer diamatic domes (DLDDs) to answer the challenges that structural engineers face in the design of this type of structure. For this purpose, 16 DLDD models with different rise-to-span ratios (RSRs) and span lengths were considered. After designing the models and performing the nonlinear time history analysis using the simultaneous effect of the three transitional components of ground motions, the target displacement at the control node was determined. Then, the pushover analysis was carried out to derive the capacity curve of the structures and calculate the seismic response modification factors in both horizontal and vertical directions. The results indicate that the domes with RSRs of 1/7 and 1/5 should be designed such that they remain in the elastic state in the horizontal direction. Then, with the growth of RSR, the value of R increases and reaches 1.792. Finally, equations were presented in this study for the period, behavior factor, and displacement amplification factor of DLDD structures in both horizontal and vertical directions using the nonlinear regression analysis.

Study on Vibration Reduction Effect of the Building Structure Equipped with Intermediate Column–Lever Viscous Damper

Generally speaking, the traditional lever amplification damping system is installed between adjacent columns in a building, which occupies a significant amount of space in the building. In contrast to amplification devices in different forms, the damper displacement of the intermediate column damper system is smaller, and the vibration reduction efficiency is lower. In light of these drawbacks, this study proposes a new amplification device for energy dissipation and vibration reduction, which is based on an intermediate column–lever mechanism with a viscous damper (CLVD). Initially, a specific simplified mechanical model of CLVD is derived. Subsequently, an equivalent Kelvin mechanical model of CLVD is derived to intuitively reflect CLVD’s damping and stiffness effect. The damping ratio added by CLVDs to the structure is calculated according to that model; the additional damping ratio and additional stiffness are utilized to calculate the displacement ratio Rd and shear force ratio Rv of the structure with CLVDs to the structure without CLVDs. Rd and Rv are introduced to evaluate the vibration reduction effect of the structure with CLVDs, and the effects of various parameters (such as intermediate column position, beam’s bending line stiffness, lever amplification factor, damping coefficient, and earthquake intensity) on Rd and Rv are analyzed. The results indicate that when the ratio of the distance from the intermediate column to the edge column to the span of the beam is 0.5, CLVD owns the optimal vibration reduction effect. Increasing the beam’s bending line stiffness is beneficial for CLVD to control structural displacement and shear force; when the leverage amplification factor is too large, the CLVD provides the structure with stiffness as the main factor, followed by damping. Additionally, when the ratio of the displacement amplification factor to the geometric amplification factor satisfies fd/γ = 1/21−0.5α, the CLVD has the optimal displacement control effect on the structure. After that, measures are provided to optimize the CLVD in different situations in order to effectively control the inter-story displacement and the story shear force of the structure. Consequently, a nine-story frame is taken as an example to elaborate the application of CLVDs in the design for energy dissipation and vibration reduction. The results reveal that the CLVD scheme adopting the proposed optimization method can effectively enhance the displacement amplification ability of CLVDs, resulting in an additional damping ratio of up to 12%. At the same time, the inter-story displacement was reduced by almost 40% under fortification earthquakes. Through the research in this study, designers can obtain a new choice in structural vibration reduction design.

Analysis of Amplification Effect and Optimal Control of the Toggle-Style Negative Stiffness Viscous Damper

This paper proposes a new toggle-style negative stiffness viscous damper (TNVD), and evaluates the performance of the TNVD with the displacement amplification factor (fd) and the energy dissipation factor (fE). Firstly, the composition and characteristics of the TNVD are introduced. Subsequently, the displacement amplification factor is introduced to evaluate the displacement amplification ability of the TNVD, and it is decomposed into a geometric amplification factor and an effective displacement coefficient. Then, based on the geometric amplification factor and effective displacement coefficient, the correlation between the TNVD’s displacement amplification ability and inter-story deformation is studied, and an improved TNVD is proposed. By the comparison of the finite element calculation results, it is found that the improved TNVD can utilize the assumption of small structural deformation. After that, the impacts of plentiful aspects, such as the length of the lower connecting rod, the horizontal inclination angle of the lower connecting rod, the inter-story deformation limit, the cross-sectional area of the connecting rod, the damping coefficient, and the negative stiffness on the fd and fE of the improved TNVD, are expounded. The research results show that when the length of the TNVD’s lower connecting rod remains unchanged, the fd and fE present a trend of increasing first and then decreasing with the increase in the horizontal inclination angle of the lower connecting rod. When the inter-story deformation is fixed, there exists an optimal lower connecting rod’s length that satisfies a specific relationship to achieve the optimal geometric amplification factor of the TNVD. By adjusting the damping parameters of the TNVD, we can obtain a better effective displacement coefficient greater than 0.95 in the proposed target region. Meanwhile, the fd and fE increase with the decrease in the negative stiffness. An optimization strategy for the improved TNVD has been proposed to ensure that the TNVD has the characteristics of operational safety, ideal displacement amplification capability, and energy dissipation capability. Furthermore, a multi-objective control design method with an additional improved TNVD structure is proposed. The vibration reduction effect of the structure with the improved TNVD and the effectiveness of the optimization strategy are verified through examples.

Seismic response modification factors of single-layer diamatic dome structures

In this research, the seismic behavior of single-layer diamatic dome (SLDD) structures was analyzed under earthquake loads, and then the seismic response modification factors (SRMFs) of these structures were extracted. For this purpose, 16 models with different span lengths (SLs) and rise-to-span ratios (RSRs) were designed, and the effects of SL and RSR on the SRMFs of these structures were evaluated. Also, the effect of member density on the SRMFs was studied. The models were first designed under the applied loads based on relevant design codes. Then, by performing the nonlinear time history analyses using the three translational components of ground motion records, the control point and target displacement in the horizontal and vertical directions were obtained to implement the pushover analyses. Thereafter, the pushover analyses were implemented by using the target displacements derived from the nonlinear time history analyses, and the SRMFs of SLDD structures in both horizontal and vertical directions were obtained. The results indicate that models with RSRs of 1/7 to 1/3 remained in the elastic range in the horizontal direction. For the models with an RSR greater than 1/3, if the RSR increases, the ductility and behavior factor increases in the horizontal direction. However, there is a downward trend in the vertical direction due to the increase in the vertical stiffness. The horizontal and vertical behavior factor was obtained in the range of 1.155–2.459 and 1.155–2.893, respectively. Finally, by using the results obtained and through the nonlinear regression analysis, equations were proposed for the period, target displacement, displacement amplification factor, and behavior factor for SLDD structures in terms of the SL and RSR in the horizontal and vertical directions.

Explicit Formulas for Optimum Parameters of Viscoelastic-type Tuned Mass Dampers

Tuned mass dampers (TMDs) are passive vibration control devices that are attached to a primary system to reduce the dynamic vibrations under exciting motion. The Voigt-type TMD, which is the most widely used one, is known as a standard model of dynamic vibration absorber (DVA). The purpose of this study is to improve the vibration control performance of passive control devices by using viscoelastic-type tuned mass dampers (V-TMDs). The study adopts the Zener model to represent the viscoelastic behavior of V-TMD. In this study, the fixed-point method is used to determine the optimum parameters of a V-TMD. The displacement amplification factor (DAF) of the coupled system is obtained in the frequency domain. The optimal parameters of the V-TMD system attached to an undamped single degree-of-freedom (sdof) main system are obtained by minimizing the DAF (symbolized with 𝛽) under the effect of base excitation. The optimum parameters, such as damping ratio (ξ) and stiffness ratio (𝜅) of the coupled system are derived, and explicit expressions corresponding to the optimum parameters are presented for engineering designs. Moreover, the change in DAF values for different mass ratios (µ) is also discussed. It is proven that V-TMD is very effective in reducing the amplitudes of vibration. The study also provides valuable insights for engineering practitioners who want to design and implement V-TMDs for vibration control applications because accurate expressions, which are simple and easy to use, are derived in order to obtain optimum parameters, and step-by-step procedures are explained.

Exploring the coupled vibration behavior of Cylindrical-Conical and Cylindrical-Exponential ultrasonic concentrators for efficient energy transfer

In this paper, the coupled vibration behavior of cylindrical-conical and cylindrical-exponential ultrasonic concentrators for efficient energy transfer is investigated. A theoretical model is developed to overcome the limitations of traditional one-dimensional theories that neglect the influence of height in the study of cylindrical concentrator vibration. Employing the equivalent elasticity method, the coupled vibration is considered as an interaction between longitudinal and plane radial vibrations. By establishing radial and longitudinal equivalent circuits with their corresponding input impedances, resonance frequency equations and the radial displacement amplification factor are derived. The effects of the radial thickness and the height-to-radius ratio on the characteristic parameters are presented for optimization designs. Numerical simulations are conducted to analyze vibrational modes and validate the theoretical findings. This study enhances the understanding of the vibration mechanism of cylindrical concentrators and provides valuable insights for selecting suitable cross-sections to improve performance and effectiveness in practical applications.

Seismic Behavior of an Innovative Four-Layer Steel Shear Wall

The steel shear wall has been introduced as a system with high stiffness and strength and a considerable capability in absorbing seismic energy. Due to its special advantages compared to other lateral load-resistant systems, this system is being used in tall buildings more and more frequently. Ductility and energy absorption are important parameters to be considered when choosing a robust lateral load-resistant system. By increasing the ductility and energy absorption of the structures, their seismic performance and safety are improved. Ideally, a structural system should provide both ductility and energy absorption in an economic way. This study presents the numerical simulation of the seismic behavior of a recently developed four-layer steel shear wall composed of corrugated and flat sheets. The simulations were performed using finite element software ABAQUS. Nonlinear static analysis was used to derive seismic parameters. The results showed that the corrugated sheets surrounded by flat sheets provide greater seismic parameters such as ductility and over-strength compared to double corrugated walls. According to the results, the calculated R-factor, displacement amplification factor, and the overstrength factor of the proposed wall were 4.58, 8.21, and 1.26, respectively. Furthermore, to use the seismic parameters of the shear wall, some relationships have been presented for incremental strength and stiffness coefficients without the need for finite element modeling. Compared to the finite element results, the presented relations had good accuracy.

Seesaw-arm energy dissipation system with U-shaped steel dampers

This paper presents an investigation of the extended seesaw system using a seesaw-arm member with U-shaped steel dampers for improving the seismic energy dissipation in building structures. One of the notable features of the existing seesaw system is its usage of a quasi-linear motion mechanism, which allows the bracing members to remain tensile during vibration. In addition, a seesaw-arm concept is proposed for magnifying the damper deformation. Evaluation methods for the lateral stiffness and strength of the proposed system were derived. Then, cyclic loading tests were performed on six specimens, revealing that the proposed system has a stable hysteretic property and large energy-dissipation capacity. The accuracy of the stiffness and strength evaluation was assessed through comparisons with the test results. The evaluation of the displacement amplification factor of the damping system agreed well with the test results. Seismic-response analyses of five-story steel frame models adopting the proposed system were conducted. The maximum story drift angle, time-history responses of displacement and energy, and plastic-hinge formation were compared with those of the bare frame model. The analysis results revealed the efficiency of the proposed system for reducing seismic responses. Furthermore, a larger shape factor of the seesaw-arm member corresponded to better seismic performance.

Seismic response modification, over-strength, and displacement amplification factors of steel special truss moment frames

In this paper, the seismic design parameters of steel special truss moment frames (STMFs), including the response modification factor (R), over-strength factor (Ω) and displacement modification factor (Cd) are evaluated for two performance levels, namely life safety (LS) and collapse prevention (CP). The effects of geometrical dimensions of the special segment located at the middle part of truss girder and the number of stories are investigated. Twelve steel STMFs with 3, 5, 7, and 9 stories with three bays are considered to evaluate the parameters. In addition, three special segment lengths are considered for each STMF. The truss-girder members are made of hollow structural sections (HSSs) and W-sections are used for columns, which are designed based on ASCE7-16 recommendations. The results show that the number of stories and the different special segment lengths affect the seismic parameters significantly. Moreover, the values obtained for R, Ω and Cd show some differences compared to the ones recommended by ASCE7-16.

An analytical solution for the dynamic response of a seawater‐sloping seabed‐bedrock system under an oblique incident P wave

AbstractMany offshore marine structures are built on seabeds with slight or considerable slopes, while most analytical studies have focused on the dynamic responses of horizontal seabeds. Based on the theory of porous media, an analytical solution for the response of a sloping seabed to earthquakes is developed in this paper. Stress and displacement responses can be shown at any location of the seabed. Using numerical examples, we analyze the influence of the slope angle, frequency and angle of incident waves, and thicknesses of the seawater and sediment layers on the dynamic response of the seabed. The results show that the solid displacement amplification factor of the surface of the horizontal seabed is always constant, while that of the sloping seabed changes periodically along the seabed surface. Even at a small site, the difference between a horizontal seabed and a sloping seabed is still significant. The slope angle has different effects on the seabed at different depths, and the inclination plays an amplification role at some depths and a reduction role at other depths. With an increase in slope angle, the difference between a horizontal seabed and a sloping seabed becomes more significant. Especially at natural frequencies, the amplification factor becomes more significant with increasing slope angle. Therefore, even though the same seawater depth is used in the model, a horizontal seabed model cannot be used to analyze the dynamic response of a sloping seabed or significant errors will occur.

Development of a novel tuned negative stiffness inerter damper for seismic induced structural vibration control

Recently, inerter-based devices have been widely explored for possible applications to both civil and mechanical engineering structures for effective vibration control. The control force-displacement relationship of an inerter is related to the vibration frequency, which may lead to excessive force under high-frequency excitation. A negative stiffness element, on the other hand, is effective for the shear force and acceleration response mitigations. The combined use of inerter and negative stiffness element therefore has the potential to further improve the control performance compared to a single device in terms of controlling both the displacement and acceleration responses. In this paper, a novel tuned negative stiffness inerter damper (TNSID) integrating negative stiffness and inerter elements is proposed for seismic induced structural vibration control. A physical realization of the proposed device is developed, and its working mechanism is analysed. The closed-form expressions for its optimal parameters are attained based on the fixed-point theory by minimizing its maximum displacement amplification factor. The proposed TNSID is then implemented to control the vibrations of a single-degree-of-freedom structure and a five-storey building subjected to different excitations to evaluate its feasibility and effectiveness. For comparison, the systems without control, with a tuned viscous mass damper, a tuned inerter damper and a negative stiffness amplifying damper are also investigated. The results reveal that the combination of the negative stiffness and inerter elements endows TNSID with the capacity to attain dual mitigation effects on both the displacement and acceleration responses and widen the effective frequency bandwidth, therefore achieve the most evident control effectiveness compared to the other devices investigated in this study.

Effects of the fluid-solid interface conditions on the dynamic responses of the saturated seabed during earthquakes

In this paper, the effects of the fluid-solid interface conditions between seawater and seabed on the dynamic responses of the seabed during earthquakes are investigated. Based on Biot's porous media theory, a semi-analytical solution of the 1D transient response and an analytical solution of the 1D steady-state response of the saturated seabed under different fluid-solid interface conditions are given, respectively. Based on the transient response solution, it is found that the fluid-solid interface conditions have a significant effect on slow waves and a small effect on fast waves. Based on the steady-state response solution, it is found that the effects of the fluid-solid interface conditions on the displacement amplification factor and pore-water pressure vary under different incident wave frequencies. In the low-frequency region, the lower the interface permeability, the smaller the displacement amplification factor. In the high-frequency region, the lower the interface permeability, the larger the displacement amplification factor. Moreover, the fluid-solid interface conditions affect the dynamic response of the seabed with different permeability coefficients to different degrees. As the seabed permeability coefficient decreases, the effects of the fluid-solid interface conditions on the dynamic responses of the seabed gradually decrease.

A novel displacement amplification factor (Cd) for steel moment-resisting frames based on performance

Displacement amplification factor is one of the most important factors in seismic design of structures. Choosing the sizes of structural section in steel moment resisting frames generally depends on the story drift limitation. In current regulations, the inelastic displacement is determined by multiplying obtained displacement out of equivalent linear static analysis by a displacement amplification factor (Cd). In this paper, several moment resisting frames have been analyzed using elastic static and inelastic dynamic analyses. After post processing of the results, a relation has been suggested for displacement amplification factor which varies along the height of the frame in three different performance levels. Three sample structures illustrate that how proposed relation improves the Cd and makes more rational results than traditional Cd. Results also show that the considered displacement amplification factor in Eurocode8 makes lower approximation of displacement.

Interpretation and evaluation of NZS1170.5 2016 provisions for seismic ratcheting

During seismic events, some structures have a tendency to ratchet and displace more in one direction than in the opposite direction after yielding, resulting in larger peak and residual displacements. Provisions to define the tendency for seismic ratcheting and the resulting displacement amplification are provided in the 2016 amendments of NZS1170.5. This paper presents some insight into the factors causing ratcheting, along with interpretation and evaluation of the proposed provisions. Firstly, the mechanics of seismic ratcheting due to dynamic stability, eccentric gravity loads, and unbalanced structural strengths in the back-and-forth directions are discussed. Afterwards, the new provisions were detailed and demonstrated by working through the NZS1170.5 commentary examples. The authors’ interpretation of the provisions is then presented, potential areas of confusion are identified, and wording changes to provide consistency and clarity are proposed. Finally, the displacement amplification factors provided in the 2016 amendments were evaluated using results of an independent study on single-degree-of-freedom reinforced concrete bridge columns subjected to eccentric gravity loading. It was found that the displacement amplification method proposed was reasonable, except when columns designed with a high ductility factor or which exhibit inelastic bilinear response had a significant tendency for ratcheting.

Seismic performance evaluation of unconfined dry stacked block masonry structure

Dry stacked block masonry is getting popularity and has auspicious future both in developed and developing countries. In this research work, it was aimed to appraise the seismic performance of unconfined dry stacked block masonry structure built with Hydraform blocks. The experimental work included the construction of a full-scale typical building and testing by using quasi-static reverse cyclic loading. The seismic parameters and behavior studied in this research work, include the force–deformation relationship, ultimate ductility factor, response modification factor, displacement amplification factor, energy dissipation, stiffness degradation, and structural performance levels. The visual assessment and analyses of the test data was scrutinized to construe and elucidate the damage patterns, and local and global behavior of the structure. Based on the results, the unconfined dry stacked block masonry structures can easily withstand against low to moderate seismic actions. The tolerance of self-interlocking blocks, in sliding and rotation in out-of-plane direction, enables it to act as energy dissipating devices and mitigates the chances of brittle shear failure.

Theoretical analysis and application research on local toggle energy dissipation device

The toggle-brace-damper system (TBDS) can obviously improve the energy dissipation efficiency of a damper by amplifying its deformation. The small deformation solution is widely used to characterize the amplification capacity of the TBDS. However, the parameters of the small deformation solution are not mutually independent. Furthermore, as the small deformation solution is a constant, it cannot comprehensively characterize the mechanism of the TBDS. These drawbacks hinder a more in-depth study of the TBDS mechanism. In addition, the existing TBDS requires a large building space, which adversely affects the layouts of doors and windows. In view of the problems above, a space-saving local toggle-brace-damper system (LTBDS), as an extended form of the TBDS, is proposed. The displacement amplification factor considering the large deformation effect is derived. The variation law of this amplification factor with the lateral displacement is clarified. The local toggle energy dissipation device (LTEDD), which consists of two identical and symmetrically arranged LTBDSs, is recommended to overcome the LTBDS’ amplification capacity asymmetry. The effects of the geometric parameters on the amplification capacity of the LTEDD are clarified. A geometric optimization method to improve the amplification capacity of the LTEDD is proposed based on the estimation of the maximum lateral displacement of the LTEDD under earthquakes. To estimate the maximum lateral displacement of the LTEDD and calculate the additional damping ratio contributed by the LTEDD damping system, the storey drift utilization ratio is proposed, and the calculation method is derived and verified. Finally, the case analysis verifies the feasibility of the LTEDD and the effectiveness of the optimization method.

Impact Response Spectrum for Vessel-Bridge Collision Design

An equivalent static method is employed in calculating the impact response of vessel-bridge collisions, in which the dynamic characteristics of vessel-bridge collisions are ignored. An impact response spectrum for vessel-bridge design is proposed according to the principle of the earthquake response spectrum. The impact force time-histories are obtained through a numerical simulation method using finite element software. The relationship between the displacement amplification factor of the single-degree-of-freedom, period, and damping ratio under the excitation of impact force-time histories is obtained. The regularity of the displacement amplification is summarized. The characteristics of the vessel-bridge collision are given. The three-stage expression and specific application steps of the impact response spectrum for the design of vessel-bridge collision are provided.

Confined hollow concrete block masonry buildings: An experimental approach for vulnerability assessment

This paper presents experimental study on the response of a sustainable structure 3.65 x3.05x3.35 m, made with confined hollow concrete block masonry (CHCBM). The model was tested under quasi-static cyclic test to assess the response against seismic load and to determine the potential vulnerability. Based on test data, envelope curves and bilinear idealized curves were drawn according to both Magenes–Calvi and Elnashai methods. Different performance levels i.e. Immediate Occupancy (IO), Life Safety (LS) and Collapse Prevention (CP) were evaluated based on both methods. Damage pattern and force-deformation behavior of CHCBM building was compared with models of the similar configuration and loading conditions. Similarly values of Response modification factor (R), Displacement Ductility (µD) and Displacement amplification factor (Cd) were calculated and compared with the previously tested models and it confirmed that CHCBM building was ductile and structurally integrated under earthquake loading.

Manufacturing, testing and simulation of novel SMA-based variable friction dampers with enhanced deformability

This study presents a novel type of self-centering damper employing NiTi Shape Memory Alloy (SMA) bars combined with variable friction mechanism for tunable hysteretic behavior and enhanced deformability. The new damper, which is called SMA-based variable friction damper (SMA-VFD), aims to significantly amplify the maximum deformability and energy-dissipation capability compared with the existing self-centering devices with tensioning SMA members. The cyclic response, phase transformation behavior, and in-situ observation of the microstructure of individual SMA bars receiving different heat treatments were first investigated to promote an adequate understanding of the link between the microscopic structure and the macroscopic property of the large size SMA bars. This is followed by a detailed discussion of the SMA-VFD, where theoretical equations as well as three performance parameters, i.e., self-centering factor γ, displacement amplification factor ω, and energy-dissipation factor λ, were derived to predict the mechanical behavior of the damper. Proof-of-concept SMA-VFD specimens were manufactured, where different preloads and friction coefficients were considered which could affect the cyclic performance. A three-dimensional finite-element model was then developed to simulate the nonlinear responses of the test specimens. Both the analytical prediction and numerical simulation exhibited good agreements with the experimental results. Utilizing the validated numerical model, the influence of manufacturing tolerance on the initial stiffness of the proposed damper was particularly investigated to help explain some important findings from the present experimental study.